The impact of the spatial legacies of spruce budworm defoliation on wildfire burn severity and post-fire recovery

Background

Boreal forests are highly complex ecosystems that are shaped by the interaction between forest structure and composition, topography, climate and weather, and disturbance regimes. This complexity causes general uncertainty around what are the particular drivers of ecosystem processes, such as wildfires. Wildfires are the primary disturbance agent that allows for forest regeneration and helps to maintain forest structure and function. Because of the central role that wildfires play in the boreal forest, it is therefore crucial to understand where they occur, why they occur and what factors influence their behaviour. Many researchers have posited that insect disturbance such as spruce budworm defoliation, which is another widespread disturbance agent across the boreal forest, has a strong impact on wildfire likelihood and behaviour by changing the abundance, structure and connectivity of combustible fuels. However, wildfires are relatively uncommon in the boreal forest, occurring on average between 50 and 200 years and the spatial legacies of insect disturbance persist just for a short window (~15 years). Additionally, both wildfires and spruce budworm defoliation affect a vast amount of area annually (give stats), therefore it is difficult to detect a small signal increas noise….

To date, current evidence on the impact of the spatial legacies of defoliation is mixed, reporting positive, negative and neutral effects. This uncertainty is in part driven by the ability to detect where particular changes in fuel or legacies of defoliation have overlapped with wildfires. Recent advances in remote sensing offers exciting prospects to utilize novel spatial data combined with thoughtful experimental design to reduce uncertainty around the effects of spruce budworm defoliation on fuels and wildfire behaviour. We are now able to remove or reduce uncertainty through better experimental design and approaches to big data problems. Here, we used a paired design within fires that have both areas that were affected by insect defoliation and not affected to attempt to resolve this uncertainty,

Questions

The overarching question is: how do the spatial legacies of spruce budworm defoliation influence wildfire burn severity and forest recovery in the boreal forest?

Specifically we will address the following questions:

  1. How does spruce budworm defoliation influence burn severity?
    1. Is there a difference in median severity between defoliated and non-defoliated fires?
    2. Is there a difference in severity extremes between defoliated and non-defoliated fires
    3. Is there a difference in variability in burn severity between defoliated and non-defoliated fires
  2. How does spruce budworm defoliation influence post-fire recovery?
    1. Is there a difference in forest recovery 10 years post-fire between defoliated and non-defoliated fires?
    2. Is there a difference in forest recovery between 1-5 years and 6-10 years between defoliated and non-defoliated fires?
  3. Is the strength of the relationship between defoliation intensity (synthetic index) and burn severity or forest recovery greater than independent metrics of defoliation?
  4. Does defoliation intensity (synthetic index) capture more variation in burn severity and forest recovery relative to defoliation metrics modeled independently?

Methods

This study focuses on wildfire that burned in the boreal shield ecoregion of Ontario. We restricted our analysis to wildfires that burned between 1986 and 2013. 1985 was chosen as the first fire year in our dataset because it is the first year that remotely sensed burn severity data are available. Similarly, our analysis of forest recovery required landsat imagery for every year for 10 years post-fire, therefore 2013 is the last year where we were able to calculate remotely sensed imagery. We identified wildfires that were defoliated up to 15 years prior to the year of fire. We chose to limit the defoliation to within 15 years because previous studies have shown that beyond 15 years, defoliation is not significant due to enhanced regrowth. We only selected fires that contained both defoliated and non-defoliated areas. Once identified, we split each fire into two distinct areas. This resulted in a total of 34 (n = 68) fires containing both defoliated and non-defoliated areas.

Structural Equation Model

The second part of the analysis looks at the effects of defoliation intensity on burn severity and forest recovery following fire. Defoliation alters fuel structure and fuel load and is expected to cause influence fire behaviour. Previous studies in Ontario have shown that defoliation can alter fire behaviour for up to 15 following defoliation [@james2017], this period is commonly referred to as the “window of opportunity”.

Spruce budworm defoliation is multivariate in nature. The effects of spruce budworm defoliation can be described by the presence and absence of defoliation, the time since defoliation to the time of fire and the number of years that an area was defoliated (a proxy for defoliation load). It is common practice for studies that concerned with the effects of spruce budworm defoliation on wildfire to use a since predictor, or build multiple sequential models to incorporate the multivariate nature of defoliation [@james2017 @james2011 @candau2018].

Structural equation models allow for the multivariate nature of defoliation by creating composite variable that allows us to combine the variation explained by multiple predictors into a synthetic index. Using structural equation models, we will combine create a synthetic index called defoliation intensity which combines defoliation presence/absence, time since defoliation and number of years defoliated.

We will fit these models to data of consisting of 34 paired defoliated/non-defoliated fires that burned in Ontario between 1986-2012. We will then model the causal effects of defoliation intensity on burn severity and forest recovery following fire. Forest recovery is measured by taking the mean composite of the normalized burn ratio for a given summer for 10 years for following fire. We then use a Theil-Sen regression to calculate the sen’s slope across the 10 years which we call the slope of recovery or forest recovery.

In our model, defoliation intensity will effect for burn severity and forest recovery. Below is the directed acyclic graph (DAG) of our a priori causal hypothesis.

In this DAG we see that time since defoliation, and number of years defoliated are combined to form the synthetic index (defoliation intensity) which is then used to predict the effects on burn severity and forest recovery. Defoliation intensity will indirectly effect forest recovery by altering stand structure and forest composition prior to fire, which will impact the number and distribution species and their seed banks that are able to establish post fire, thus affecting the recovery trajectory. Similarly, defoliation intensity will effect burn severity by either increasing or decreasing severity which will lead to a change in the recovery trajectory by either increasing or decreasing the slope of recovery.

Preliminary results

How does spruce budworm defoliation influence burn severity?

## Loading required package: gt
Results from Pairwise T-test on severity between defoliated and non-deoliated
Test t-value df P-value
Median Severity -2.16095466572192 69 0.034
Extreme Severity 1.13546435208255 69 0.260
Variability in Severity 0.960918785574236 69 0.340

Severity visualization

How does spruce budworm defoliation influence post-fire recovery?

Results from Pairwise T-test on Slope of Recovery Between Defoliated and Non-Deoliated
Test t-value df P-value
10yr post-fire -0.190211446294039 32 0.850
1-5yr post-fire 0.116163538758242 32 0.908
6-10yr post-fire -1.17872274643132 32 0.247

Slope visualization

targets::tar_read(lolliplot_slope)

Is there a difference in the direction of the effects ?

chisq_table(targets::tar_read(chisq_result))
Significant Difference in Direction of Trend between Paired Fires
Results from chi-square tst
Independent Variable of Interest x² df P-value
Median Severity 0.457 1 0.499
Extreme Severity 0.029 1 0.865
Varibility in Severity 2.857 1 0.091
10 yr slope of recovery 0.061 1 0.806
1-5 yr slope of recovery 2.970 1 0.085
6-10 yr slope of recovery 0.545 1 0.460

Does a synthetic index of defoliation intensity capture more variation in burn severity and forest recovery relative to defoliation metrics modelled using an interaction? Are the strengths of the effects different?

First, we fit repeated measures linear mixed effects models with an interaction terms between time since defoliation and cumulative years of defoliation for each response variable:

\(Y_{i} = \beta_0 + \beta_1X_{1i} + \beta_2X_{2i} +\beta_3X_{1i}X_{2i} + u_{i} \epsilon_{i}\).

Where Y = the response variable of interest and i = for the i th fire, \(\beta_1X_{1i}\) = time since disturbance (tsd), \(\beta_2X_{2i}\) = cumulative years of defoliation (cyd), \(+\beta_3X_{1i}X_{2i}\) = interaction between tsd and cyd, \(u_{i}\) = random intercept for paired fire id.

Median Severity

Median Burn Severity
Results from repeated measures hierachical linear mixed model fit in nlme
term estimate std.error df statistic p.value
(Intercept) 148.5519561 13.564996 69 10.95112401 0.000
tsd 0.1194051 2.221304 67 0.05375453 0.957
cumltve_yrs -5.6309938 7.704273 67 -0.73089228 0.467
tsd:cumltve_yrs 1.7565995 1.268738 67 1.38452499 0.171

Extreme Severity

Burn Severity Extremes
Results from repeated measures hierachical linear mixed model fit in nlme
term estimate std.error df statistic p.value
(Intercept) 431.015128 15.198599 69 28.358872 0.000
tsd -5.696929 1.924455 67 -2.960281 0.004
cumltve_yrs -4.128863 6.749045 67 -0.611770 0.543
tsd:cumltve_yrs 2.268256 1.119966 67 2.025289 0.047

Variability in Severity

Variability in Burn Severity
Results from repeated measures hierachical linear mixed model fit in nlme
term estimate std.error df statistic p.value
(Intercept) 0.885112852 0.075651726 69 11.6998368 0.000
tsd -0.016773176 0.013062859 67 -1.2840356 0.204
cumltve_yrs 0.021500616 0.045119739 67 0.4765235 0.635
tsd:cumltve_yrs 0.001450466 0.007408573 67 0.1957821 0.845

Slope of recovery 10 year

Slope of Recovery 1-10 Years Post-Fire
Results from repeated measures hierachical linear mixed model fit in nlme
term estimate std.error df statistic p.value
(Intercept) 2.245057626 0.47873528 69 4.6895596 0.000
tsd -0.016706872 0.03091348 67 -0.5404397 0.591
cumltve_yrs -0.024095691 0.10932424 67 -0.2204058 0.826
tsd:cumltve_yrs 0.008397846 0.01824350 67 0.4603200 0.647

Slope of recovery 1-5 year

Slope of Recovery 1-5 Years Post-Fire
Results from repeated measures hierachical linear mixed model fit in nlme
term estimate std.error df statistic p.value
(Intercept) 2.209471809 0.92553266 69 2.3872435 0.020
tsd -0.086667287 0.08157811 67 -1.0623841 0.292
cumltve_yrs 0.256959955 0.28784754 67 0.8926946 0.375
tsd:cumltve_yrs 0.004341114 0.04796296 67 0.0905097 0.928

Slope of recovery 6-10 year

Slope of Recovery 6-10 Years Post-Fire
Results from repeated measures hierachical linear mixed model fit in nlme
term estimate std.error df statistic p.value
(Intercept) 2.737738986 1.12219988 69 2.4396180 0.017
tsd 0.008386609 0.06743685 67 0.1243624 0.901
cumltve_yrs -0.189328806 0.23856683 67 -0.7936091 0.430
tsd:cumltve_yrs 0.027194831 0.03981959 67 0.6829511 0.497

SEM RESULTS

Significance

Land managers in the boreal forest region require information about burn severity to address immediate hazards and outcomes resulting from wildfires. Understanding how previous disturbance history shapes patterns of burn severity is needed to guide management activities and ensure downstream ecosystem provisioning when threatened by multiple disturbances. Results from this chapter will provide a framework for modelling the effects of spruce budworm defoliation on wildfire severity and help managers identify areas that are at the highest risk of losing valuable ecosystem services.